Distinct speed and direction memories of migrating dendritic cells diversify their search strategies

Migrating cells exhibit various motility patterns, resulting from different migration mechanisms, cell properties, or cell-environment interactions. The complexity of cell dynamics is reflected, e.g., in the diversity of the observed forms of velocity autocorrelation function-which has been widely served as a measure of diffusivity and spreading. By analyzing the dynamics of migrating dendritic cells in vitro, we disentangle the contributions of direction θ and speed v to the velocity autocorrelation. We find that the ability of cells to maintain their speed or direction of motion is unequal, reflected in different temporal decays of speed and direction autocorrelation functions, AC_v(t)∼t^-1.2 and AC_θ(t)∼t^-0.5, respectively. The larger power-law exponent of AC_v(t) indicates that the cells lose their speed memory considerably faster than the direction memory. Using numerical simulations, we investigate the influence of AC_θ and AC_v as well as the direction-speed cross correlation C_θ-v on the search time of a persistent random walker to find a randomly located target in confinement. Although AC_θ and C_θ-v play the major roles, we find that the speed autocorrelation AC_v can be also tuned to minimize the search time. Adopting an optimal AC_v can reduce the search time even up to 10% compared with uncorrelated spontaneous speeds. Our results suggest that migrating cells can improve their search efficiency, especially in crowded environments, through the directional or speed persistence or the speed-direction correlation.